If you are looking for actual history books my go to author is Adrian Goldsworthy. My favourite book of his is The Fall of Carthage which deals in all the Punic Wars which really puts the Roman Republic on the map. Another one of his which I like is Antony and Cleopatra which is a biography of Antony's rise and fall and his relationship with the Egyptian queen. I would also highly recommend his biography on Caesar which I have to say is the best one I've read.

if you're looking for some books written by some men from back then I would suggest The Conquest of Gaul by Caesar himself. The book is excellent and tells you exactly how the Roman legions lived and campaigned back in those days, and it's also fun that many soldiers are mentioned by name (like Lucius Vorenus and Titus Pullo).

The Histories By Polybius is also a good book. His goal was to describe Rome's rise and a few reasons why they became so powerful. It's most famous section however deals in explaining the Roman constitution.

For the Greek part I am not so knowledgeable, but I have read some books and I can provide som suggestions. History of the Peloponnesian War by Thucydides, which is a book written by a Greek general. Is discusses the war between Sparta and Athens which began in 431 BC. On Sparta By Plutarch deals in Spartan customs and culture, and is a major source for knowledge about the city's rise and fall.

As a warning to be used when reading ancient material; Don't take all the books as a direct source for history as exaggerating and changing course of events was common and an acceptable way of writing history back then, particularly I would say Livy is one who is very prone the this. I would say that Polybius is one of the more thrustworthy ones (or at least so does Mr. Goldsworthy claim in one of his books). If you're writing a paper or something about the subject I suggest reading modern material about the subject.

I don't read much mythology, but I have read both the Oddesey and the Illiad, and while I didn't find them easy reads, I think they'll be to your tasting.

While I'm just a huge history buff who's studying history at the moment I hope this helps. Excuse my grammar mistakes if there are any. English is not my first language.

I recommend two books. I took some Roman courses in college and found the two textbooks my professor issued to be fantastic if you want and easy read and are just starting off. If you want a light, yet extremely informative history of Rome I suggest, The Romans: From Village to Empire: A History of Rome from the Earliest Times to the Empire by Mary T Boatwright and others. Very informative; touches on many if not most of the important chronology of Rome. Also if you are interested in the culture and customs of the Romans, as well as interesting myths and stories that shaped their society I suggest, As the Romans Did: A Sourcebook in Roman Social History, 2nd Edition by Jo-Ann Shelton. Very interesting facets of Roman life that offers context to any Ancient Roman topic.

For mythology a great place to start would be Edith Hamelton's Mythology.

http://www.amazon.com/Mythology-Timeless-Tales-Gods-Heroes/dp/0446574759

It has been pretty much a go to introductory book for Greco-Roman mythology for decades.

For ancient writers, I wholeheartedly suggest you go for Homer for the Illiad and The Odyssey. Virgil's Aeneid is also a fun read.

For historical fiction I am surprised nobody has mentioned I, Claudius by Robert Graves.

There's a wealth of resources for both [Ancient Greece] (http://www.reddit.com/r/AskHistorians/wiki/books/europe#wiki_ancient_greece) and [Ancient Rome] (http://www.reddit.com/r/AskHistorians/wiki/books/europe#wiki_ancient_rome) on the Ask Historians Book list.

Herodotus's Histories (Greece, 440 B.C.E.) is truly fascinating and one of my all time favorite books. It's considered one of the first written "history" books. I am linking to the Wikipedia post here only because it does give a good overview of all the wonderful things he covers. http://en.wikipedia.org/wiki/Histories_%28Herodotus%29

You can get the book for yourself in several places on the net, including the MIT Internet Classics Archive: http://classics.mit.edu/Herodotus/history.html

Also, the Romans practically worshipped Virgil, who based his Aeneid on Homer's classics. It's one of the most important books for scholars of Latin and Roman history. Even today if you go to Italy you'll find that many many people know parts of the Aeneid by heart, having been required to memorize it in school. Plus it's just a cool story too. http://classics.mit.edu/Virgil/aeneid.html

For mythology - Homer's Iliad and Odyssey have some good references to myths, from what I've heard in my college classes those two along with Hesiod's Theogony are the best first-hand resources for it.

Greek Tragedy (specifically the big three - Aeschylus, Sophocles and Euripides) is also great reading for Greeks. They make many references to mythology. What's interesting to note is that we are able to read only approx. 10% of tragedy written for the Festival of Dionysus, the rest have been lost to time.

For my University-level introductory Archaic and Classical Greek History Class, we read "Ancient Greece" by Thomas Martin. Fantastic, clear, well-written book that covers many of the main topics from the Paleolithic Age through Alexander. I recommend it.

From a fiction standpoint, I can recommend some excellent books. Conn Iggulden has a series on Caesar that I really enjoyed. It does take liberties of course, but it's not bad.

For historical fiction in general, Bernard Cornwell is fantastic. He hasn't done anything on Rome, but I had to mention him because he's just so damned good. Because of him I went from having zero interest in history to having history become one of my hobbies.

Also, surprisingly Spartacus was more historically accurate than you might think. Yes, of course there were numerous inaccuracies and liberties taken, but overall it's quite good. Thanks to that series I actually learned a lot about Spartacus and his contemporaries. Note, I supplemented the info in the show with actual research, but still the show gave me the framework I needed to make the names into real people.